Geostatistical modelling of spatial distribution of Balaenoptera physalus in the Northwestern Mediterranean Sea from sparse count data and heterogeneous observation efforts

Obtaining accurate maps of relative abundance is an objective that may be difficult to achieve on the basis of spatially heterogeneous observation efforts and infrequent and sparse animal sightings. However, characterizing spatial distribution of wild animals such as fin whales is a major priority to protect these populations and to study their interactions with their environment. We have associated a geostatistical model with the Poisson distribution to model both spatial variation and discrete observation process. Assuming few weak hypotheses on the distribution of abundance, we have improved the experimental variogram estimate using weights that are derived from expected variances and proposed a bias correction that accounts for the variability added by the Poisson observation process. In the same way the kriging system was modified to interpolate directly the theoretical underlying animal abundance better than noisy observations from count data. For cumulative count data of fin whales over the summers 1993–2001, the method gave a map of the relative abundance which is informative on the spatial patterns. Kriging interpolation variances were dramatically reduced – ratio from 0.015 to 0.26 – compared to usual Ordinary Kriging on raw data. Adding the hypothesis of stationarity over time the variogram estimated on cumulative data can be then used with more sparser annual data.